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TOPOLOGICAL CONDITIONS OF NI NEAR-RINGS

Dheena, P.;Jenila, C.

  • Received : 2011.12.23
  • Published : 2013.10.31

Abstract

In this paper we introduce the notion of NI near-rings similar to the notion introduced in rings. We give topological properties of collection of strongly prime ideals in NI near-rings. We have shown that if N is a NI and weakly pm near-ring, then $Max(N)$ is a compact Hausdorff space. We have also shown that if N is a NI near-ring, then for every $a{\in}N$, $cl(D(a))=V(N^*(N)_a)=Supp(a)=SSpec(N){\setminus}int\;V(a)$.

Keywords

NI near-ring;strongly prime ideal;weakly pm near-ring;symmetric near-ring

References

  1. G. F. Birkenmeier, J. Y. Kim, and J. K. Park, Regularity conditions and the simplicity of prime factor rings, J. Pure Appl. Algebra 115 (1997), no. 3, 213-230. https://doi.org/10.1016/S0022-4049(96)00011-4
  2. P. Dheena and D. Sivakumar, On strongly 0-prime ideals in near-rings, Bull. Malays. Math. Sci. Soc. (2) 27 (2004), no. 1, 77-85.
  3. S. U. Hwang, Y. C. Jeon, and Y. Lee, Structure and topological conditions of NI rings, J. Algebra 302 (2006), no. 1, 186-199. https://doi.org/10.1016/j.jalgebra.2006.02.032
  4. J. Lambek, On the representations of modules by sheaves of factor modules, Canad. Math. Bull. 14 (1971), 359-368. https://doi.org/10.4153/CMB-1971-065-1
  5. G. Marks, On 2-primal Ore extensions, Comm. Algebra 29 (2001), no. 5, 2113-2123. https://doi.org/10.1081/AGB-100002173
  6. G. Marks, A taxonomy of 2-primal rings, J. Algebra 266 (2003), no. 2, 494-520. https://doi.org/10.1016/S0021-8693(03)00301-6
  7. J. R. Munkres, Topology, Prentice-Hall of India, New Delhi, 2005.
  8. G. Pilz, Near-Rings, North-Holland, Amsterdam, 1983.
  9. K. Samei, The zero-divisor graph of a reduced ring, J. Pure Appl. Algebra 209 (2007), no. 3, 813-821. https://doi.org/10.1016/j.jpaa.2006.08.008
  10. S. H. Sun, Noncommutative rings in which every prime ideal is contained in a unique maximal ideal, J. Pure Appl. Algebra 76 (1991), no. 2, 179-192. https://doi.org/10.1016/0022-4049(91)90060-F